Free Energy and Thermodynamics - Scf

“Free Energy
and
Thermodynamics”
Chapter 17
First
Law
of
Thermodynamics
• First
Law
of
Thermodynamics:

Energy
cannot
be
Created
or
Destroyed
– the
total
energy
of
the
universe
cannot
change
– though
you
can
transfer
it
from
one
place
to
another
• ΔE universe 
=
0
=
ΔE system 
+
ΔE surroundings
First
Law
of
Thermodynamics
• Conserva>on
of
Energy
• For
an
exothermic
reac>on,
“lost”
heat
from
the
system
goes
into
the
surroundings
• two
ways
energy
“lost”
from
a
system,
– converted
to
heat,
q
– used
to
do
work,
w
• Energy
conserva>on
requires
that
the
energy
change
in
the
system
equal
the
heat
released
+
work
done
– 
ΔE
=
q
+
w
– 
ΔE
=
ΔH
+
PΔV
• 
ΔE
is
a
state
func,on
– internal
energy
change
independent
of
how
done
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1

Energy
Tax
• You
can’t
break
even!
• To
recharge
a
baLery
with
100
kJ
of
useful
energy
will
require
more
than
100
kJ
• Every
energy
transi>on
results
in
a
“loss”
of
energy
– conversion
of
energy
to
heat
which
is
“lost”
by
hea>ng
up
the
surroundings
Heat
Tax
Thermodynamics
and
Spontaneity
• Thermodynamics
predicts
whether
a
process
will
proceed
under
the
given
condi>ons
– spontaneous
process
• nonspontaneous
processes
require
energy
input
to
go
• Spontaneity
is
determined
by
comparing
the
free
energy
of
the
system
before
the
reac>on
with
the
free
energy
of
the
system
aPer
reac>on.
• Spontaneity
≠
fast
or
slow
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Comparing
Poten>al
Energy
The
direc>on
of
spontaneity
can
be
determined
by
comparing
the
poten>al
energy
of
the
system
at
the
start
and
the
end.
Thermodynamics
vs.
Kine>cs
Factors
Affec>ng
Whether
a
Reac>on
Is
Spontaneous
• The
two
factors
that
determine
the
thermodynamic
favorability
are
the
enthalpy
and
the
entropy.
• The
enthalpy
is
a
comparison
of
the
bond
energy
of
the
reactants
to
the
products.
– bond
energy
=
amount
needed
to
break
a
bond.
– 
ΔH
• The
entropy
factors
relates
to
the
randomness/
orderliness
of
a
system
– 
ΔS
• The
enthalpy
factor
is
generally
more
important
than
the
entropy
factor
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Enthalpy
• Related
to
the
internal
energy
• 
ΔH
generally
kJ/mol
• Stronger
bonds
=
more
stable
molecules
• If
products
more
stable
than
reactants,
energy
released
– exothermic
– 
ΔH
=
nega>ve
• If
reactants
more
stable
than
products,
energy
absorbed
– endothermic
– 
ΔH
=
posi>ve
• The
enthalpy
is
favorable
for
exothermic
reac>ons
and
unfavorable
for
endothermic
reac>ons.
• Hess’
Law

ΔH° rxn
=
Σ(ΔH° prod)
‐
Σ(ΔH° react)
Entropy
• Entropy
is
a
thermodynamic
func>on
that
increases
as
the
number
of
energe>cally
equivalent
ways
of
arranging
the
components
increases,
S
• S
generally
J/mol
• S
=
k
ln
W
– k
=
Boltzmann
Constant
=
1.38
x
10 ‐23 
J/K
– W
is
the
number
of
energe>cally
equivalent
ways,
unitless
• Random
systems
require
less
energy
than
ordered
systems
• Energe>cally
Equivalent
States
for
the
Expansion
of
a
Gas
W
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Macrostates

Microstates
• These
microstates
all
have
the
same
macrostate
• So
there
are
6
different
par>cle
arrangements
that
result
in
the
same
macrostate
Macrostates
and
Probability
• There
is
only
one
possible
arrangement
that
gives
State
A
and
one
that
gives
State
B
• There
are
6
possible
arrangements
that
give
State
C
• Therefore
State
C
has
higher
entropy
than
either
State
A
or
State
B
• The
macrostate
with
the
highest
entropy
also
has
the
greatest
dispersal
of
energy
Changes
in
Entropy,
ΔS
• Entropy
change
is
favorable
when
the
result
is
a
more
random
system.
– 
ΔS
is
posi>ve
• Some
changes
that
increase
the
entropy
are:
– reac>ons
whose
products
are
in
a
more
disordered
state.
• (solid
>
liquid
>
gas)
– reac>ons
which
have
larger
numbers
of
product
molecules
than
reactant
molecules.
– increase
in
temperature
– solids
dissocia>ng
into
ions
upon
dissolving
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Increase
in
Entropy
The
2 nd
 Law
of
Thermodynamics
• The
total
entropy
change
of
the
universe
must
be
posi>ve
for
a
process
to
be
spontaneous
– for
reversible
process
ΔS univ 
=
0,
– for
irreversible
(spontaneous)
process
ΔS univ 
>
0
• 
ΔS universe
=
ΔS system
+
Δs surroundings
• If
the
entropy
of
the
system
decreases,
then
the
entropy
of
the
surroundings
must
increase
by
a
larger
amount
– when
ΔS system 
is
nega>ve,
ΔS surroundings
 is
posi>ve
• The
increase
in
ΔS surroundings
oPen
comes
from
the
heat
released
in
an
exothermic
reac>on
Entropy
Change
in
State
Change
• When
materials
change
state,
the
number
of
macrostates
it
can
have
changes
as
well
– for
entropy:
solid

Entropy
Change
and
State
Change
Heat
Flow,
Entropy,
and
the
2 nd 
Law
• Heat
must
flow
from
water
to
ice
in
order
for
the
entropy
of
the
universe
to
increase
Temperature
Dependence
of
ΔS surroundings
• When
a
system
process
is
exothermic,
it
adds
heat
to
the
surroundings,
increasing
the
entropy
of
the
surroundings
• When
a
system
process
is
endothermic,
it
takes
heat
from
the
surroundings,
decreasing
the
entropy
of
the
surroundings
• The
amount
the
entropy
of
the
surroundings
changes
depends
on
the
temperature
it
is
at
originally
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Gibbs
Free
Energy,
ΔG
• Maximum
amount
of
energy
from
the
system
available
to
do
work
on
the
surroundings
G
=
H
–
T∙S
ΔG sys 
=
ΔH sys 
–
TΔS sys
ΔG sys 
=
–
TΔS universe
ΔG reacGon 
=
Σ
nΔG prod 
–
Σ
nΔG react
• When
ΔG
on
C 3 H 8(g) 
+
5
O 2(g)
 
→
3
CO 2(g) 
+
4
H 2 O (g) 
has
ΔH rxn 
=
‐2044
kJ
at
25°C.
Calculate
the
entropy
change
of
the
surroundings
Free
Energy
Change
and
Spontaneity
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Gibbs
Free
Energy,
ΔG
• Process
will
be
spontaneous
when
ΔG
is
nega>ve
• ΔG
will
be
nega>ve
when
– 
ΔH
is
nega>ve
and
ΔS
is
posi>ve
• exothermic
and
more
random
– 
ΔH
is
nega>ve
and
large
and
ΔS
is
nega>ve
but
small
– 
ΔH
is
posi>ve
but
small
and
ΔS
is
posi>ve
and
large
• or
high
temperature
• 
ΔG
will
be
posi>ve
when
ΔH
is
+
and
ΔS
is
−
– never
spontaneous
at
any
temperature
• 
When
ΔG
=
0
the
reac>on
is
at
equilibrium
ΔG,
ΔH,
and
ΔS
Example
• The
reac>on
CCl 4(g)
→
C (s,
graphite)
+
2
Cl 2(g)
has
ΔH
=
+95.7
kJ
and
ΔS
=
+142.2
J/K
at
25°C.
Calculate
ΔG
and
determine
if
it
is
spontaneous.
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The
3 rd 
Law
of
Thermodynamics
Absolute
Entropy
• The
absolute
entropy
of
a
substance
is
the
amount
of
energy
it
has
due
to
dispersion
of
energy
through
its
par>cles
• The
3 rd 
Law
states
that
for
a
perfect
crystal
at
absolute
zero,
the
absolute
entropy
=
0
J/mol∙K
– therefore,
every
substance
that
is
not
a
perfect
crystal
at
absolute
zero
has
some
energy
from
entropy
– therefore,
the
absolute
entropy
of
substances
is
always
+
Standard
Entropies
• S°
• Extensive
• Entropies
for
1
mole
at
298
K
for
a
par>cular
state,
a
par>cular
allotrope,
par>cular
molecular
complexity,
a
par>cular
molar
mass,
and
a
par>cular
degree
of
dissolu>on
Rela>ve
Standard
Entropies
States
• The
gas
state
has
a
larger
entropy
than
the
liquid
state
at
a
par>cular
temperature
• The
liquid
state
has
a
larger
entropy
than
the
solid
state
at
a
par>cular
temperature
Substance
S°,
(J/mol·K)
H 2O (g) 70.0
H 2O (l) 188.8
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Rela>ve
Standard
Entropies
Molar
Mass
• The
larger
the
molar
mass,
the
larger
the
entropy
• Available
energy
states
more
closely
spaced,
allowing
more
dispersal
of
energy
through
the
states
Rela>ve
Standard
Entropies
Allotropes
• The
less
constrained
the
structure
of
an
allotrope
is,
the
larger
its
entropy
Rela>ve
Standard
Entropies
Molecular
Complexity
• Larger,
more
complex
molecules
generally
have
larger
entropy
• More
available
energy
states,
allowing
more
dispersal
of
energy
through
the
states
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Rela>ve
Standard
Entropies
Dissolu>on
• Dissolved
solids
generally
have
larger
entropy
• Distribu>ng
par>cles
throughout
the
mixture
Example
S°,
Substance
(J/mol·K)
KClO3 (s) 143.1
KClO 3 (aq) 265.7
• Calculate
ΔS°
for
the
reac>on
4
NH 3(g) 
+
5
O 2(g) 
→
4
NO (g) 
+
6
H 2 O (l)
Calcula>ng
ΔG°
• At
25°C:
ΔG o reac>on 
=
ΣnGo f (products)
‐
ΣnGo f (reactants)
• At
temperatures
other
than
25°C:
– assuming
the
change
in
ΔH o reac>on 
and
ΔSo reac>on 
is
negligible
ΔG° reacGon 
=
ΔH° reacGon 
–
TΔS° reacGon
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Example
• Calculate
ΔG°
at
25°C
for
the
reac>on
CH 4(g) 
+
8
O 2(g) 
→
CO 2(g) 
+
2
H 2 O (g) 
+
4
O 3(g)
ΔG
Rela>onships
• If
a
reac>on
can
be
expressed
as
a
series
of
reac>ons,
the
sum
of
the
ΔG
values
of
the
individual
reac>on
is
the
ΔG
of
the
total
reac>on
– ΔG
is
a
state
func>on
• If
a
reac>on
is
reversed,
the
sign
of
its
ΔG
value
reverses
• If
the
amounts
of
materials
is
mul>plied
by
a
factor,
the
value
of
the
ΔG
is
mul>plied
by
the
same
factor
– the
value
of
ΔG
of
a
reac>on
is
extensive
Free
Energy
and
Reversible
Reac>ons
• The
change
in
free
energy
is
a
theore>cal
limit
as
to
the
amount
of
work
that
can
be
done
• If
the
reac>on
achieves
its
theore>cal
limit,
it
is
a
reversible
reac>on
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• In
a
real
reac>on,
some
of
the
free
energy
is
“lost”
as
heat
– if
not
most
• Therefore,
real
reac>ons
are
irreversible
Real
Reac>ons
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